Q62. - Algebra 2

Question

Prove the Power of a Product Property,${\left(ab\right)}^m=a^m{b}^m$  .

Step-by-Step Solution

Answer

It is proved that${\left(ab\right)}^m=a^m{b}^m$  .

Step 1. Given Information.

Given to prove the Power of a Product Property ${\left(ab\right)}^m=a^m{b}^m$ .

Step 2. Explanation .

Rewriting the given expression:

 $\begin{array}{l}{\left(ab\right)}^m=ab\times ab\times ab\times \mathrm{...}\text{m times}\\ {\left(ab\right)}^m=a\times b\times a\times b\times a\times b\times \mathrm{...}\text{m times}\\ {\left(ab\right)}^m=(a\times a\times a\mathrm{...}\text{ m times})\times (b\times b\times b\times \mathrm{...}\text{m times})\\ {\left(ab\right)}^m=a^m{b}^m\end{array}$

Step 3. Conclusion .

Hence, It is proved that${\left(ab\right)}^m=a^m{b}^m$  .